This invention is related to the field of white light phase shifting interferometry. Phase-shifting interferometry (PSI) has proven to be a highly accurate and efficient method for the measurement of single reflective surfaces in a variety of applications including optical testing, surface profilometry, surface roughness estimation, and surface displacement measurement. PSI was first introduced by Bruning et al. in 1974, Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses, Applied Optics 13, 2693-26703 (1974).
The fundamental concept of PSI is that the phase of an interferogram can be extracted by acquiring a set of a few sequentially phase-shifted interferograms of the original interferogram with a constant phase shift between any two adjacent interferograms (or intensity frames). These phase shifted interferograms are produced by changing the optical path difference (OPD) between a measurement surface and a reference surface, or by changing the wavelength if the OPD is not zero. Thus, all types of PSI measurements rely on some mechanism to shift or change the phase of an interferogram in a regular and predictable manner.
PSI also has been successfully applied to measure an object with multiple reflective surfaces, such as a transparent plate, which produces multiple interferograms superimposed on the recording plane of an interferometer. Such systems are disclosed in the U.S. patent to S. Tang U.S. Pat. No. 6,885,461, and the articles to P. DeGroot, Measurement of Transparent Plates with Wavelength-tuned Phase Shifting Interferometry, Applied Optics, Vol. 39, No. 16, 2658-2663 (2000) and K. Okada et al. Separate Measurements of Surface Shapes and Reflective Index Inhomogeneity of an Optical Element Using Tunable Source Phase Shifting Interferometry, Applied Optics, Vol. 29, No. 22, 3280-3285 (1990). Each of the interferograms from transparent plates carries topographic information related to its corresponding reflective surface. The phase of each interferogram in the superimposed interferograms shifts at a different speed during the wavelength changes. Consequently, each interferogram is differentiated from the others; and its phase may be extracted from the set of superimposed interferograms, as disclosed in the U.S. patent to S. Tang U.S. Pat. No. 6,856,405.
As disclosed in the Tang '405 patent, in order to obtain precise estimates for the various surface phases, phase shift increments between any two adjacent intensity frames must be calibrated to a known constant. While this condition is desirable for the phase measurement of a single surface, it becomes essential when multiple overlapping interferograms are present and the phase contribution from each reflective surface must be segregated from the other surfaces.
Since 1990, PSI with a spectrally broad band or white light illumination known as vertical scanning interferometry also has been widely used to profile surfaces. Although white light phase shifting interferometry (WLPSI) is capable of measuring surfaces with nanometer precision and with step height greater than one-fourth of a wavelength, the technique is only able to profile objects with uniform surface properties, and without transparent thin films. This is because the complex surface properties, such as bulk surfaces, single or multi-layer film stacks on a substrate, unresolved micro-structures on a substrate, or as part of a film stack, from the testing object create various phase shifts on reflections. Typically, WLPSI loses its ability to profile such objects.
With the introduction of temporal interferometric signal modeling techniques in WLPSI recently, an object with complex surface properties can be measured with improved precision. This signal modeling technique not only obtains the topographic information of the test surface, but also simultaneously or separately determines additional parameters of the test piece, e.g. layer thickness and/or material refractive index for film stacks, or line width and structure depth of micro-structures. Signal modeling techniques may acquire a set of white light phase-shifted interferograms with piezoelectric transducer (PZT) pushers of either the reference flat or the test object. Signal modeling techniques require a constant phase shift between any adjacent interferograms similar to measuring a transparent plate with a tunable laser in PSI. However, the material properties of a PZT cause the phase of interferogram change to be non-linear with respect to the time during the acquisition. Such non-linear phase shifts result in errors in sampling the temporal interferometric signal at each pixel of the interferograms. Such sampling errors greatly deteriorate the measurement accuracy of the signal modeling technique.